In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

In this paper, we study some properties of the near SR-compactnessin L-topological spaces, where L is a fuzzy lattice. The near SR-compactness isa kind of compactness between Lowen’s fuzzy compactness and SR-compactness,and it preserves desirable properties of compactness in general topologicalspaces.

in this paper, we study some properties of the near sr-compactnessin l-topological spaces, where l is a fuzzy lattice. the near sr-compactness isa kind of compactness between lowen’s fuzzy compactness and sr-compactness,and it preserves desirable properties of compactness in general topologicalspaces.

Lattice actions and topological charges that are classically and quantum mechanically perfect (i.e. free of lattice artifacts) are constructed analytically for the quantum rotor. It is demonstrated that the Manton action is classically perfect while the Villain action is quantum perfect. The geometric construction for the topological charge is only perfect at the classical level. The quantum pe...

The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson–Dirac operator, or equivalently, as the index of Neuberger’s lattice Dirac operator, is shown to have analogous properties to Lüscher’s geometrical lattice topological charge. The main new result is that it reduces to the continuum topological charge in the classical continuum lim...

Electrons hopping on the sites of a three-dimensional pyrochlore lattice are shown to form topologically nontrivial insulating phases when the spin-orbit (SO) coupling and lattice distortions are present. Of 16 possible topological classes 9 are realized for various parameters in this model. Specifically, at half-filling an undistorted pyrochlore lattice with a SO term yields a "pristine" stron...

We define topological orthoalgebras (TOAs), and study their properties. While every topological orthomodular lattice is a TOA, the lattice of projections of a Hilbert space (in its norm or strong operator topology) is an example of a lattice-ordered TOA that is not a topological lattice. On the other hand, we show that every compact Boolean TOA is a topological Boolean algebra. We also show tha...

Topological indices are the real number of a molecular structure obtained via molecular graph G. Topological indices are used for QSPR, QSAR and structural design in chemistry, nanotechnology, and pharmacology. Moreover, physicochemical properties such as the boiling point, the enthalpy of vaporization, and stability can be estimated by QSAR/QSPR models. In this study, the QSPR (Quantitative St...

We investigate the large deformation and extreme load-management capabilities of a soft topologically polarized kagome lattice mapped to cylindrical domain through problem wheel rolling on an irregular surface. test surface–lattice interaction experimentally by subjecting 3D-printed topological prototype localized distributed boundary loads. This investigation reveals dichotomy in force transfe...